High School

Solve the problem:

The maximum weight for an elevator is 1600 pounds. You need to move boxes, each weighing 145 pounds. Write an inequality that can be used to determine the maximum number of boxes you can place in the elevator at one time. Assume only you and the boxes are in the elevator.

A. [tex]1600 - 145 \leq 40n[/tex]

B. [tex]145 + 40n \geq 1600[/tex]

C. [tex]145 + 40n \leq 1600[/tex]

D. [tex]1600 + 145 \geq 40n[/tex]

Answer :

To solve this problem, we need to determine the maximum number of boxes, each weighing 145 pounds, that can fit in an elevator with a maximum capacity of 1600 pounds. Let's assume that only you and the boxes are in the elevator, and for this problem, we can ignore your weight.

Let's define:
- [tex]\( n \)[/tex] as the number of boxes.

The weight of the boxes in the elevator can be expressed as:
[tex]\[ 145 \times n \][/tex]

The total weight of the boxes must be less than or equal to the maximum capacity of the elevator, which is 1600 pounds. Therefore, the inequality is:
[tex]\[ 145 \times n \leq 1600 \][/tex]

Now let's check the answer choices to see which one matches this inequality:

- Choice a: [tex]\( 1600 - 145 \leq 40n \)[/tex]
- Choice b: [tex]\( 145 + 40n \geq 1600 \)[/tex]
- Choice c: [tex]\( 145 + 40n \leq 1600 \)[/tex]
- Choice d: [tex]\( 1600 + 145 \geq 40n \)[/tex]

The correct matching inequality from the list that resembles our derived inequality [tex]\( 145n \leq 1600 \)[/tex] is choice c: [tex]\( 145 + 40n \leq 1600 \)[/tex].